Description of the courses for Fall 2019 are posted here

Spring 2020 courses

M380D Algebra

It is assumed that students know the basic material from an undergraduate course in linear algebra and an undergraduate abstract algebra course. The first part of the Prelim examination will cover sections 1 and 2 below. The second part of the Prelim examination will deal with section 3 below.

M381D Complex Analysis

The objective of this syllabus is to aid students in attaining a broad understanding of analysis techniques that are the basic stepping stones to contemporary research. The prelim exam normally consists of eight to ten problems, and the topics listed below should provide useful guidelines and strategy for their solution. It is assumed that students are familiar with the subject matter of the undergraduate analysis courses M365C and M361. The first part of the Prelim examination will cover Real Analysis. The second part of the prelim examination will cover Complex Analysis.

M382D Differential Topology

It is assumed that students have a working knowledge of the equivalent of a one semester course in general topology (for example, see the appended syllabus for the undergraduate course M367K). For the semester in differential topology, it will also be assumed that students know the basic material from an undergraduate linear algebra course. The first part of the Prelim examination will deal with Algebraic Topology and the second part will deal with Differential Topology.

M383D Methods of Applied Mathematics

It is assumed that students are familiar with the subject matter of the undergraduate analysis course M365C (see the Analysis section for a syllabus of that course) and an undergraduate course in linear algebra.

The Applied Math Prelim divides into these six areas. The first three are discussed in M383C and will be covered in the first part of the Prelim examination:

Weak laws of large numbers (Sections 1.5, 1.6): the L2 -weak law of large numbers, triangular arrays, Borel-Cantelli lemmas, modes of convergence, inequalities (Markov, Chebyshev, Jensen, Hölder), the weak law of large numbers